There were several periods where certain people tried to institute reforms to the Chinese Communist system, but they were not particularly successful until after Mao died. The leaders between Mao's death and now realized that reforms were needed to feed the country and to produce the amount of goods and wealth that they wanted. The began to free the markets (to some extent) and gradually expanded economic freedom, leading to the system we see today. I would caution that they are not exactly capitalist because the government is still very invasive and controlling. However, they have certainly gone very far down that path compared to where they were through the 1970s.

Some Examples of Reform:

Deng Xiaoping

-Split up the communes into family units -Peasants sold their excess in markets -Shift away form heavy industry and a shift towards consumer goods industrially -Special Economic Zones: zones where foreign industries could establish enterprises and maintain a degree of economic freedom -China became more open to the west. Westerners came in to teach and other jobs while Chinese went abroad in increasing numbers. -Deng de-emphasized proper ideology for schooling and placed more of an emphasis on talent and hard work.

Jiang Zemin

-The government largely abandoned price controls -2/3 of the market was guided by private forces -Private enterprises outperformed state-owned enterprises -Joined the WTO in 2001

Hu Jintao

-Major foreign investment continues

tl;dr China slowly decreased direct government control of the markets and allowed more private enterprise to flourish as well as opening up to the west.

Source: Grasso, June, Jay Corrin, and Michael Kort. Modernization and Revolution in China: From the Opium Wars to the Olympics. Armonk, New York: M.E. Sharpe, 2009.

edit: Minor formatting